Comparison of information structures in zero-sum games

This note provides simple necessary and sufficient conditions for the comparison of information structures in zero-sum games. This solves an open problem of Grossner and Mertens [Gossner, O., Mertens, J.-F., 2001. The value of information in zero-sum games. http://ogossner.free.fr/Articles/abstract.pdf]. The conditions are phrased in terms of Blackwell garbling of information of each of the players.     

Intertemporal Equity and Efficient Allocation of Resources

Competitive paths which are efficient are shown to satisfy a terminal cost minimization condition, thereby providing a continuous-time counterpart to the discrete-time result due to Malinvaud. Using this result, competitive paths which are equitable and efficient are shown to satisfy Hartwick's investment rule, which states that the value of net investment is zero at each date. Our result indicates that Hartwick's rule can help to signal inefficiency of competitive equitable paths. Journal of Economic Literature Classification Numbers: C61, D90, O41.     

On Forward Induction and Evolutionary and Strategic Stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by E. van Damme (1989, J. Econ. Theory48, 476-496) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) capture this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (J. Swinkels, 1992, J. Econ. Theory57, 306-332) is always consistent with forward induction. Journal of Economic Literature Classification Number: C72.     

On the Welfare Significance of National Product for Economic Growth and Sustainable Development

This paper formulates an investment value transversality condition in a continuous-time growth model, which characterizes competitive paths along which current net national product measures the welfare achieved along the path. This transversality condition requires that the present value of net investment goes to zero asymptotically. An example provided shows that, in general, competitive paths do not necessarily satisfy this condition. It is also shown that, in a standard growth model including an exhaustible resource as an essential factor of production, competitive paths always satisfy this condition. Implications regarding national income accounting procedures and sustainable development policies are discussed.
JEL Classification Numbers: D90; O11; O41; Q32.     

Job Matching and Coalition Formation with Utility or Disutility of Co-workers

This paper studies the job matching market in Kelso and Crawford (1982), Econometrica50, 1483–1504, with one exception, that co-workers may generate utility or disutility in the workplace. We provide a simple idea to show how a great number of sufficient conditions for a nonempty core in the literature can be extended to this labor market. A generalized competitive equilibrium with a tax/subsidy system is also discussed. Journal of Economic Literature Classification Number: D71.     

Extension of Oi's price instability theorem

Oi's theorem that product price variability raises the average profit of a single-product perfectly competitive firm is generalized in this paper to cover the case of an n-commodity firm. Under similar conditions to those mentioned by Oi for the single-product case, commodity (factor or product) price instability raises the average profit of an n-commodity perfectly competitive firm.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

Responsive pricing

We study the efficiency property of responsive pricing, a scheme that proposes to increase prices as a function of the level of capacity utilization in environments where traditional allocation schemes (e.g. competitive markets, non-linear pricing) cannot be implemented in practice. We show that although responsive pricing implements allocations that are arbitrarily close to full capacity utilization (no wasted capacity and no excess demand), these allocations are not always efficient. We identify conditions under which efficiency occurs and discuss implications for the use of responsive pricing. We would like to thank seminar participants at the LSE, Venezia, Toulouse, and Copenhagen as well as Piero Gottardi, Karel Mertens, Marco Ottaviani, Markus Poschke, Karl Schlag, and Sanne Zwart for useful comments.     

The Identification of Preferences from Equilibrium Prices under Uncertainty

The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individuals under uncertainty; this is the case even if the asset market is incomplete. Journal of Economic Literature Classification Numbers: D52, D80.     

Type space on a purely measurable parameter space

Summary. Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Harsányi suggested the concept of the type space. Later Mertens and Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure.Received: 12 August 2002, Revised: 1 March 2004, JEL Classification Numbers: C70, C79, D80, D82.Miklós Pintér: The author wishes to thank Péter Tallos, Tamás Solymosi, and an anonymous referee for their suggestions and comments. This work was supported by OTKA grant T046194.     

On the computation of stable sets and strictly perfect equilibria

Summary. In this paper a procedure is described that computes for a given bimatrix game all stable sets in the sense of Kohlberg and Mertens (1986). Further the procedure is refined to find the strictly perfect equilibria (if any) of such a game. Recieved: December 29, 1999; revised version: February 17, 2000     

Investment options and the business cycle

This paper extends [R. Mehra, E.C. Prescott, Recursive competitive equilibrium: The case of homogeneous households, Econometrica 48 (1980) 1365-1380] to a production economy with two capital goods. It is an RBC model in which each unit of investment requires a new idea, an ‘option.’ When options are scarce, new capital is harder to put in place and the value of old capital rises. Thus the stock market and Tobin's Q are negative indexes of intangibles. During a boom, Q rises gradually, as options are used up. Because investment represents an exercise of options, it has an intertemporal substitution tradeoff that is absent from the adjustment-cost model. Equilibrium may be efficient even without markets for knowledge; the stock market may suffice.     

Private Value Allocations in Large Economies with Differential Information

We consider a Radner-type (e.g., Radner, 1968, Econometrica36, 31–58) pure exchange economy with differential information and a continuum of agents. We show that under appropriate assumptions the set of Aumann–Shapley private value allocations in such an economy coincides with the set of Radner competitive equilibrium allocations. Journal of Economic Literature Classification Numbers: C71, D51, D82.     

Discounting and welfare evaluation of policies

We start with the premise that if policy discounting is to have any welfare relevance, one has to accept it being a derivative of a social welfare function (SWF). We show that if that derivative is to have a net present value (NPV) form, then the baseline allocation must be stationary. In addition, we show that at a stationary baseline in an overlapping generations growth economy, the intergenerationally fair discount rate equals the growth rate of per‐capita consumption, which is, roughly, 2% for the United States. This differs from the interest rate, even in the golden rule equilibrium, unless population growth is null. The last result is based on the main theorem in Mertens and Rubinchik (2012) and is demonstrated for a policy space that might naturally arise in applications.     

Message spaces for perfect correlated equilibria

Summary. We show that a perfect correlated equilibrium distribution of an N-person game, as defined by Dhillon and Mertens (1996) can be achieved using a finite number of copies of the strategy space as the message space.Received: 31 August 2004, Revised: 1 April 2005, JEL Classification Numbers: C72.Srihari Govindan: Correspondence toGovindan would like to thank the Social Sciences and Humanities Research Council of Canada for research support.     

The small worlds axiom for stable equilibria

The small worlds axiom was introduced in J. F. Mertens (Math. Oper. Res. 16, (1991)) with the meaning that, if the payoffs to a subset of the players are unaffected by the actions of the outsiders (or if just their best reply correspondence is unaffected), the solutions (the stable sets) of the game between insiders are exactly the projections of the solutions of the larger game. We prove this property here for q-stable sets, for any characteristic q.     

Prices, Delay, and the Dynamics of Trade

We characterize the dynamics of trading patterns and market composition when trade is bilateral, finding a trading partner is costly, prices are determined by bargaining, and preferences are private information. We show that equilibrium is inefficient and exhibits delay as sellers price discriminate between buyers with different values. As frictions vanish, transaction prices are asymptotically competitive and the welfare loss of inefficient trading approaches zero, even though the trading patterns continue to be inefficient and delay persists. Journal of Economic Literature Classification Numbers: D40, D50.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Can a larger market foster R&D under monopolistic competition with variable mark-ups?

We study monopolistic competition with symmetric directly additive preferences (generating variable mark-ups) and an endogenous technology choice. Each firm chooses an investment in R&D to decrease its marginal cost. We prove that the equilibrium R&D investment increases with market size (a larger population or trade) only if the price-elasticity of demand is an increasing function. Together with the output levels, such equilibrium investments may be socially excessive or insufficient, depending on whether the elasticity of the subutility is increasing or decreasing. The main implication is that opening up to free trade can foster R&D through variable mark-ups.     

Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exists and is unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a lattice based approach to the problem. The class of economies for which we are able to obtain our existence and uniqueness result is considerably larger than those considered in previous work. We conclude by applying the new results to some important examples of monetary economies often used in applied work. Journal of Economic Literature Classification Numbers: C62, D51, D90, E10.